Simplify the following expression: $r = \dfrac{10q^2 - 130q + 400}{q - 8} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $10$ , so we can rewrite the expression: $ r =\dfrac{10(q^2 - 13q + 40)}{q - 8} $ Then we factor the remaining polynomial: $q^2 {-13}q + {40} $ ${-8} {-5} = {-13}$ ${-8} \times {-5} = {40}$ $ (q {-8}) (q {-5}) $ This gives us a factored expression: $\dfrac{10(q {-8}) (q {-5})}{q - 8}$ We can divide the numerator and denominator by $(q + 8)$ on condition that $q \neq 8$ Therefore $r = 10(q - 5); q \neq 8$